1. The orbit in which the moon revolves [intersects] the orbit in which the sun revolves at an angle,¹More specifically, as mentioned in Halachah 9, the maximum angular distance between the two orbits is 5 degrees. [so that] a portion of [the moon's orbit] is inclined to the north of the sun's orbit and a portion is inclined south of the sun's orbit.²The importance of the concept the Rambam introduces here, the difference in latitude between the planes of the orbits of the sun and the moon, becomes significant in the following chapter.

To explain briefly: In the previous chapters, it was explained that the visibility of the moon depends upon the distance in longitude between it and the sun. At the time of conjunction, the sun and the moon are at the same longitudinal point. Therefore, they set at the same time. As the difference in longitude between them increases, the crescent of the moon grows and the time of its setting becomes later, increasing the chances of its visibility.

Nevertheless, the moon's latitude also affects its visibility. The greater the latitude of the moon [i.e., its inclination from the orbit of the sun] the larger its crescent will appear. Also, a northerly latitude causes the moon to set later and thus makes it easier to be sighted. A southerly latitude, by contrast, causes the moon to set earlier and thus makes sighting it more difficult. There are two points, one opposite the other, at which these orbits intersect.³The difference in latitude between the orbits of the sun and the moon explains why there is not a lunar eclipse at every full moon, and why there is not a solar eclipse at every conjunction - although at the time of the full moon, the sun, the earth and the moon are aligned in a single line, and at the time of conjunction, the sun, the moon and the earth are aligned in a single line.

Although the longitude of the sun and the moon is the same at these times, since their latitudes are different, the moon's shadow does not interfere with the light of the sun at a conjunction, and the earth's shadow does not prevent the light of the sun from reaching the moon at a full moon. Only when a conjunction or a full moon takes place at (or near) the point where the orbits of the moon and the sun intersect does an eclipse take place.

When the moon is at one of these points, it is revolving in the same plane as the sun. As the moon departs from these points, it is proceeding either to the north or to the south of the sun.

The point in the moon's [orbit] at which it begins to be inclined to the north of [the plane of] the sun's [orbit] is referred to as the head, while the point [in its orbit] from which it begins to be inclined to the south of [the plane of] the sun's [orbit] is referred to as the tail.*

This head revolves at a uniform pace,⁴Because of the revolution of the head, the determination of the moon's longitude will require several stages of computation. [proceeding] in opposition to the movement of the sphere of the constellations⁵I.e., the head revolves from east to west. without increase or decrease - i.e., it moves from [the constellation of] Pisces to [the constellation of] Aquarius. It continuously follows [this pattern].

2. The mean movement of the head in one day is 3 minutes and 11 seconds.⁶As evident from the later figures given by the Rambam, this number is an approximation, and the actual figure is several thirds less. Thus, its movement in ten days is 31 minutes and 47 seconds; its movement in one hundred days is 5 degrees, 17 minutes, and 43 seconds, in symbols 5° 17' 43". In one thousand days, its movement is 52 degrees, 57 minutes and 10 seconds, in symbols 52° 57' 10". The remainder [of the sum] of its progress in ten thousand days is 169 degrees, 31 minutes and 40 seconds, in symbols 169° 31' 40".

Thus, the distance it travels in twenty-nine days is 1 degree, 32 minutes and 9 seconds, in symbols 1° 32' 9". Its progress in a regular year is 18 degrees, 44 minutes and 42 seconds, in symbols 18° 44' 42". The mean position of the head on Thursday night [of the present year,] the starting point for these calculations, is 180 degrees, 57 minutes, and 28 seconds, in symbols 180° 57' 28".⁷The Rambam is giving a negative figure here, his intent being 360° - 180° 57' 28. In positive terms, it would be a position of 179° 2' 32.

3. If you desire to calculate the position of the head at any given date, [you should follow this procedure:] First, calculate the mean progress of the head as you calculated the mean of the sun and the mean of the moon. [Afterwards,] subtract this mean from 360 degrees,⁸This subtraction is necessary, since, as mentioned above, the head revolves from east to west, opposite to the direction of the heavenly sphere as a whole.

Thus, we begin with a negative value as a starting point and add to it the distance traveled by the head. When that total is subtracted from 360, we have a positive figure that is the true position of the head. The reason the Rambam uses a negative figure for his starting point is that as the numbers increase, it is easier to add the mean distance traveled by the head to the starting point of 180° 57' 28 and subtract the total from 360, than to define the starting point in positive terms and subtract the mean progress from it. and the remainder will be the location of the head at that time. The tail's position will always be the [place in the moon's orbit] directly opposite it.

4. What is implied? Let us suppose that we desired to know the location of the head on Friday night, the second of Iyar of this year - the starting point for these calculations. There are 29 complete days between the night of the starting point and the date for which we desire to know the location of the head.

5. We should then calculate the mean of the head according to the familiar manner, adding its distance traveled in 29 days to the starting point. Thus, the mean of the head is 182 degrees, 29 minutes and 37 seconds, in symbols 182° 29' 37". This mean should be subtracted from 360, leaving a remainder of 177 degrees, 30 minutes and 23 seconds, in symbols 177° 30' 23".

This is the location of the head. The seconds are of no consequence. Thus, the position of the head will be 27 degrees and 30 minutes within the constellation of Virgo. The position of the tail will be [directly] opposite it: 27 degrees and 30 minutes within the constellation of Pisces.

6. There will always be an even half of the celestial sphere between the position of the head and the position of the tail. Therefore, whenever the head is in a particular constellation, the tail will be seven constellations further in the order of constellations, at the same position with regard to degrees and minutes. For example, if the head is ten degrees within a particular constellation, the tail will be ten degrees within the seventh constellation from it.

7. After having established the position of the head, the position of the tail, and the true position of the moon, consider [these three figures]: If the position of the moon is the same, both in degrees and in minutes, as its head or tail, then the moon will not be inclined to the north or the south.⁹As mentioned previously, the head and the tail are the positions where the moon's orbit intersects with that of the sun. Thus, if the moon is at the head or the tail, it is not at all inclined.

If the position of the moon has passed¹⁰We have used a non-literal translation of the word ינפל in this and the following sentence based on the context in this halachah. the head¹¹I.e., the difference between the position of the moon and the position of the head is less than 180 degrees, as stated in Halachah 10. and it is proceeding in the direction of the tail, know that the moon will be inclined to the north of the [plane] of the sun's [orbit]. If the position of the moon is before the tail¹²I.e., the difference between the position of the moon and the position of the head is more than 180 degrees, as stated in Halachah 10. and it is proceeding in the direction of the head, know that the moon will be inclined to the south of the [plane] of the sun's [orbit].

8. The inclination of the moon to the north or to the south is referred to as the moon's latitude.¹³The Hebrew term רחב הירח literally means "the width of the moon." It was given this name because its range from 0° to 5° is far less than that of the longitude of the moon, ארך הירח, the angular distance between the moon and the sun, which ranges from 0° to 360°. If the moon's incline is northerly, it is referred to as a northerly latitude. If the moon's incline is southerly, it is referred to as a southerly latitude. If the moon is positioned at either [the head or the tail], it has no latitude, as explained above.

9. The moon's latitude¹⁴According to contemporary science, the Rambam is making an approximation, for the latitude of the moon can reach 5 degrees and 9 minutes. will never exceed five degrees, whether to the north or to the south. This is the pattern it follows. [The moon] begins at the head and diverges slightly [from the sun's orbit, as it proceeds on its own orbit]. [The size of] this divergence continues to increase until it reaches five degrees.¹⁵As indicated from Halachah 11, this is the mid-point between the head and the tail, 90° and 270°. At this point, [the moon] begins to come slightly closer [to the sun's orbit], until it has no latitude at all when it reaches its tail.

[After it reaches the tail, the moon] will again begin to diverge slightly [from the sun's orbit], until this divergence reaches five degrees. It will then begin to approach [the sun's orbit], until ultimately it has no latitude at all.

10. [The following procedure should be applied] if you desire to determine the latitude of the moon, and to [know] whether it is northerly or southerly: First, calculate the position of the head and the true position of the moon at the desired date. Then subtract the position of the head from the true position of the moon. The remainder is referred to as "the course of the latitude."¹⁶I.e., the distance the moon has traveled in its orbit from the head to its present position.

If the course of the latitude is between one degree and 180 degrees, the latitude of the moon is northerly. If course of the latitude is more than 180 degrees, the latitude of the moon is southerly. If [the course] is an even 180 degrees or an even 360 degrees, the moon does not have any latitude at all.

Afterwards, determine the size of the angle of the course of the latitude¹⁷This refers to the angle between the plane of the sun's orbit and the position of the moon in its orbit. - i.e., the extent to which the moon is inclined to the north or to the south. This figure is referred to as the moon's southerly latitude or northerly [latitude], as we explained.

11. How large is the angle of the course of the latitude? If the course of the latitude is ten degrees, its angle will be 52 minutes. If the course is twenty degrees, its angle will be one degree and 43 minutes. If the course is thirty degrees, its angle will be 2 degrees and 30 minutes.

If the course is forty degrees, its angle will be 3 degrees and 13 minutes. If the course is fifty degrees, its angle will be 3 degrees and 50 minutes. If the course is sixty degrees, its angle will be 4 degrees and 20 minutes. If the course is seventy degrees, its angle will be 4 degrees and 42 minutes. If the course is eighty degrees, its angle will be 4 degrees and 55 minutes. If the course is ninety degrees, its angle will be 5 degrees.¹⁸As stated above, this is the greatest latitude reached.

12. If [the course of the latitude] has both units and tens, you should [calculate the average increase per degree and add the proportionate amount to the lower figure], as was done with regard to the course of the sun and the course of the moon.¹⁹See Chapter 13, Halachah 7, and Chapter 15, Halachah 7.

What is implied? When the course of the latitude is 53 degrees, [the size of the angle should be determined as follows]. It has already been established that when the course is 50 degrees, its angle is 3 degrees and 50 minutes. When the course is 60 degrees, its angle is 4 degrees and 20 minutes. Therefore, there is a difference of 30 minutes between them, 3 minutes for each degree. Accordingly, [when] calculating the angle for a course of 53 degrees, [the result] will be 3 degrees and 59 minutes. A similar process should be followed with regard to all other figures.

13. Since you know the angles for all the values of the course of the latitude until ninety degrees, as was mentioned, you will be able to know the angle for all possible values of the course. For if the course is between 90 and 180 degrees, subtract the course from 180 and find the angle for the remainder.²⁰For, as mentioned above, 90 degrees is the even mid-point of the course, and its angle increases and decreases in the same proportions as one approaches or leaves that point.

14. ²¹In the standard printed texts of the Mishneh Torah, there is a printing error, and the concluding phrase from the chapter was added here by mistake.Similarly, if the course is between 180 and 270 degrees,²²At 270°, as at 90°, the course reaches its maximum latitude, 5 degrees. subtract 180 from [the course] and find the angle for the remainder.²³For, as mentioned above, the course begins to increase as it progresses after reaching its tail in the same proportions as it increases as it progresses from its head.

15. Similarly, if the course is between 270 and 360 degrees, subtract [the course] from 360 and find the angle for the remainder.²⁴For the rate of the angular decrease from 270 to 180 is equivalent to the rate of decrease from 90 to 180.

16. What is implied? If the course is 150°, subtract 150 from 180, leaving 30. As mentioned previously, the angle [of a course] of 30 [degrees] will be 2 degrees and 30 minutes. Thus, the angle [of a course] of 150 [degrees] also will be 2 degrees and 30 minutes.

17. If the course is 200°, subtract 180 from 200, leaving 20. As mentioned previously, the angle [of a course] of 20 [degrees] will be 1 degree and 43 minutes. Thus, the angle [of a course] of 200 [degrees] also will be 1 degree and 43 minutes.

18. If the course is 300°, subtract 300 from 360, leaving 60. As mentioned previously, the angle [of a course] of 60 [degrees] will be 4 degrees and 20 minutes. Thus, the angle [of a course] of 300 [degrees] also will be 4 degrees and 20 minutes. A similar process should be followed with regard to all other values.

19. [The following procedure should be applied] if one desires to know the latitude of the moon and whether it is either northerly or southerly at the beginning of Friday night, the second of Iyar of this year: It has already been established that the true position of the moon on this night is 18 degrees and 36 minutes within the constellation of Taurus, in symbols 18° 36". [Similarly, it has been established that] the position of the head at that time is 27 degrees and 30 minutes within the constellation of Virgo, in symbols 27° 30'.

[To arrive at the latitude,] you must subtract the position of the head from the position of the moon, leaving a course of the latitude of 231 degrees and 6 minutes, in symbols 231° 6'. [As mentioned,] the minutes are of no consequence with regard to the course. Therefore, according to the principles explained in this chapter, the angle of this course will be 3 degrees and 53 minutes. This is the latitude of the moon at the beginning of this night. It is southerly, for the course is larger than 180 degrees.